Depending upon the receiver you get altitude as either MSL (above sea level) or altitude above the geoid (ususally WGS84). A few receivers let you select either. Most don't document which one they use. Heather tries to force the WGS84 which the GPS system provides and is more consistent. Conversion to MSL is done differently by every receiver. The conversion is done via who know what mathematical model of the geoid. The difference between WGS84 and MSL altitude can be up to 100 meters. If you force a position into the device you want to use whatever altitude the receiver uses... which may or may not be apparent. There are web sites that can do the conversions (but who knows what model the web site and receiver are using)
The lat/lon/alt values that different receivers provide in survey or position hold mode is device dependent. Some provide "live" values, some provide filtered, averaged, or fixed values. Most telecom type GPSDOs don't provide a way to get back to providing "live" values once they have a fixed position available.